WASHINGTON (AP) — Senate Republicans blocked another of President Barack Obama’s picks for one of the nation’s top courts on Tuesday, the latest skirmish in a nominations battle that has intensified partisan tensions in the chamber.

The vote derailed Obama’s selection of Georgetown University law professor Cornelia Pillard to fill one of three vacancies on the U.S. Court of Appeals for the District of Columbia Circuit. The roll call was 56-41 in favor of ending GOP procedural delays that have blocked Pillard from winning confirmation — four short of the 60 votes Democrats needed.

The D.C. circuit court is considered one of the nation’s most powerful because it rules on administration orders and regulations and because some of its judges ultimately become Supreme Court justices. The D.C. circuit’s eight current judges are divided evenly between Democratic and Republican nominees.

Democrats used Tuesday’s vote to assail Republicans for opposing female nominees to the D.C. circuit. Republicans have blocked votes on two other Obama nominees to the same court this year, attorneys Patricia Millett and Caitlin Halligan.

“Women are grossly underrepresented on our federal courts. So what kind of message are Senate Republicans sending by refusing to even allow a vote on three of the most qualified female attorneys in this country,” Senate Judiciary Committee Chairman Patrick Leahy, D-Vt., said.

Iowa Sen. Charles Grassley, top Republican on the Judiciary panel, called such arguments “offensive,” adding that Democrats’ “last line of defense is to accuse Republicans of opposing nominees based upon gender or race.”

Tuesday’s vote prompted Democrats to threaten anew to unilaterally rewrite Senate rules to make it harder for the chamber’s minority party to block nominations. Democrats could do that by curbing a minority’s ability to require 60 votes to end procedural delays called filibusters.

It is unclear that Democrats have enough votes to force such changes. Some senior lawmakers have long warned that it would boomerang against them should the GOP recapture the Senate majority and the White House.

In a sign of shifting attitudes, Leahy — a senator for nearly four decades — said he now backs a rules change because blocking judges for political reasons “destroys the integrity of the federal judiciary.”

Sens. Susan Collins of Maine and Lisa Murkowski of Alaska were the only two Republicans to vote “yes” on Pillard. Senate Majority Leader Harry Reid, D-Nev., was the only Democrat to vote “no,” allowing him to stage the vote again.

Senate Minority Leader Mitch McConnell, R-Ky., called the Pillard vote “a political exercise designed to distract the American people from the mess that is Obamacare,” a reference to major enrollment problems with the 2010 health care law. White House spokesman Jay Carney said Republicans were making “cynical arguments in an effort to maintain an ideological edge” among judges on the D.C. circuit.

Republicans have accused Obama of trying to tilt the court's balance in his direction to protect the fate of his administration’s policies. They say the D.C. circuit has a lighter caseload than other districts, and have proposed legislation eliminating one of its vacant judgeships and moving the two others to busier circuits.

Democrats say the GOP objections are purely political and that Republicans did not object to filling D.C. circuit vacancies when George W. Bush was president. They cite other statistics to argue that the D.C. circuit’s workload has changed little in recent years.

Pillard worked twice in the administration of President Bill Clinton — at the solicitor general's office, which handles Supreme Court cases, and later in the Justice Department. She’d previously worked for the NAACP Legal Defense and Educational Fund, and has argued nine cases before the Supreme Court.

Another Obama nominee for the D.C. circuit, U.S. District Judge Robert Wilkins, is expected to be considered by the Senate in coming days and seems likely to be blocked.